Fractal-Related Multiscale Geometric Characterisation of Topographies

In this chapter, the basic natures of fractalsFractal and multiscale characterisations are discussed, and practical applications of these fractal-related methods for useful characterisations of surface topography are examined. Length-scale, area-scale and curvature-scale fractal-related analysisFractal analysis methods are examined in detail because these methods have demonstrated value for industrial and scientific applications. Length- and area-scale methods are described in ASME and ISO specification standards. The context and rationale for using fractal-related multiscale geometric analysis for describing surface topography are examined first, then followed by discussion of the chaotic nature of measured surface topographies and the future of multiscale geometric characterisation. Length-, area-, and curvature-scale analysis methods, which exploit the fractal natures of topographies, are reviewed, with an emphasis on areal methods. Curvature-scale analyses and characterisations are presented with example applications and a discussion of their potential. In addition, examples of functional correlations, and abilities to discriminate that are made possible by multiscale geometric analysis, are presented.